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A157722 Primes of the Form : p1=a*b+c;p2=a*c+b;p3=b*c+a;p=(p1+p2+p3)/2; p1,p2 and p3 are three consecutive prime numbers. 1
43, 863, 1181, 3467, 10613, 23081, 26189, 27803, 42407, 138731, 463949, 630167, 702101, 1038731, 1417649, 1452851, 2005061, 2060921, 4925861, 6565721, 9709163, 9739721, 10047881, 14268113, 15515573, 16575113, 16615031, 17300873, 17382461 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

lst={}; Do[a=Prime[n]; b=Prime[n+1]; c=Prime[n+2]; x=a*b+c; y=a*c+b; z=b*c+a; p=(x+y+z)/2; If[PrimeQ[p], AppendTo[lst, p]], {n, 1, 7!}]; lst

prf[{a_, b_, c_}]:=Module[{x=a*b+c, y=b*c+a, z=a*c+b, k}, k=(x+y+z)/2; If[PrimeQ[ k], k, 0]]; DeleteCases[prf/@Partition[Prime[Range[500]], 3, 1], 0] (* Harvey P. Dale, May 12 2016 *)

CROSSREFS

Sequence in context: A229689 A146979 A278174 * A010959 A161668 A162181

Adjacent sequences:  A157719 A157720 A157721 * A157723 A157724 A157725

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Mar 04 2009

STATUS

approved

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Last modified May 22 18:53 EDT 2019. Contains 323481 sequences. (Running on oeis4.)